Department of Mathematics, Tamkang University, New Taipei 25137, Taiwan.
Stat Med. 2013 May 30;32(12):2001-12. doi: 10.1002/sim.5656. Epub 2012 Oct 10.
Motivated by an epidemiological survey of fracture in elderly women, we develop a semiparametric regression analysis of current status data with incompletely observed covariate under the proportional odds model. To accommodate both the interval-censored nature of current status failure time data and the incompletely observed covariate data, we propose an analysis based on the validation likelihood (VL), which is derived from likelihood pertaining to the validation sample, namely the subset of the sample where the data are completely observed. The missing data mechanism is assumed to be missing at random and is explicitly modeled and estimated in the VL approach. We propose implementing the VL method by integrating self-consistency and Newton-Raphson algorithms. Asymptotic normality and standard error estimation for the proposed estimator of the regression parameter are guaranteed. Simulation results reveal good performance of the VL estimator. The VL method has some gain in efficiency compared with the naive complete case method. But the VL method leads to unbiased estimators, whereas the complete case method does not when missing covariates are not missing completely at random. Application of the VL approach to the fracture data confirms that osteoporosis (low bone density) is a strong risk factor for the age at onset of fracture in elderly women.
受老年女性骨折的流行病学调查的启发，我们在比例优势模型下，为不完全观测协变量的现状数据开发了半参数回归分析。为了同时适应现状失败时间数据的区间删失性质和不完全观测协变量数据，我们提出了一种基于验证似然（VL）的分析方法，该方法源自验证样本（即数据完全观测的样本子集）的似然。假设缺失数据机制是随机缺失的，并在 VL 方法中明确建模和估计。我们提出通过整合自一致性和牛顿-拉普森算法来实现 VL 方法。对于回归参数的建议估计量，保证了渐近正态性和标准误差估计。模拟结果表明 VL 估计量具有良好的性能。与简单的完全病例方法相比，VL 方法在效率上有一定的提高。但是，当缺失协变量不是完全随机缺失时，VL 方法会导致无偏估计量，而完全病例方法不会。VL 方法在骨折数据中的应用证实，骨质疏松症（骨密度低）是老年女性骨折发病年龄的一个强有力的危险因素。
